Evolution Equations In Mathematical Physics Research Articles

Variable-Coefficient Hyperbola Function Method and Its Application to (2+1)-Dimensional Variable-Coefficient Broer-Kaup System**The project supported by National Natural Science Foundation of China under Grant No. 10072013 and the State Key Basic Research Development Program under Grant No. G1998030600

Based on a new intermediate transformation, a variable-coefficient hyperbola function method is proposed. Being concise and straightforward, it is applied to the (2+1)-dimensional variable-coefficient Broer–Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2+1)-dimensional Broer–Kaup system are given. The method can be applied to other variable-coefficient nonlinear evolution equations in mathematical physics.

Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation**The project supported by National Natural Science Foundation of China under Grant No. 10072013 and the State Key Basic Research Development Program under Grant No. G1998030600

By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.

Variable-coefficient projective Riccati equation method and its application to a new (2+1)-dimensional simplified generalized Broer–Kaup system

Abstract In this paper, based on a new intermediate transformation, a variable-coefficient projective Riccati equation method is proposed. Being concise and straightforward, it is applied to a new (2 + 1)-dimensional simplified generalized Broer–Kaup (SGBK) system. As a result, several new families of exact soliton-like solutions are obtained, beyond the travelling wave. When imposing some condition on them, the new exact solitary wave solutions of the (2 + 1)-dimensional SGBK system are given. The method can be applied to other nonlinear evolution equations in mathematical physics.

Exact travelling wave solutions for the Boiti–Leon–Pempinelli equation

Abstract By using an improved projective Riccati equation method, several types of exact travelling wave solutions to the Boiti–Leon–Pempinelli equation are obtained which include kink-shaped soliton solutions, singular soliton solutions and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.

New soliton-like solutions to the potential Kadomstev–Petviashvili (PKP) equation

In this paper, new soliton-like solutions are obtained for (2+1)-dimensional potential Kadomstev–Petviashvili (PKP) equation by using the symbolic computation method developed by Gao and Tian. Solitary wave solutions obtained in [Appl. Math. Comput 123 (2001) 29] are merely a special case in this paper. The method can also be extended to other types of nolionear evolution equations in mathematical physics.

Constructing families of soliton-like solutions to a (2+1)- dimensional breaking soliton equation using symbolic computation

The application of computer algebra to science has a bright future. In this paper, using computerized symbolic computation, new families of soliton-like solutions are obtained for (2+1)- dimensional breaking soliton equations using an ansatz. These solutions contain traveling wave solutions that are of important significance in explaining some physical phenomena. The method can also be applied to other types of nonlinear evolution equations in mathematical physics.

The extended Jacobian elliptic function expansion method and its application in the generalized Hirota–Satsuma coupled KdV system

In this paper an extended Jacobian elliptic function expansion method, which is a direct and more powerful method, is used to construct more new exact doubly periodic solutions of the generalized Hirota–Satsuma coupled KdV system by using symbolic computation. As a result, sixteen families of new doubly periodic solutions are obtained which shows that the method is more powerful. When the modulus of the Jacobian elliptic functions m→1 or 0, the corresponding six solitary wave solutions and six trigonometric function (singly periodic) solutions are also found. The method is also applied to other higher-dimensional nonlinear evolution equations in mathematical physics.

Symbolic computation and new families of exact soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2+1)-dimensional spaces

In this paper, new families of soliton-like solutions are obtained for (2+1)-dimensional integrable Broer-Kaup equations by using the symbolic computation method developed by Gao and Tian. Sample solutions obtained from these methods are presented. Solitary wave solutions are merely a special case in one family. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.

On a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution equations in mathematical physics

According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer.